A Simple Model of Plate Generation from Mantle Flow
A Simple Model of Plate Generation from Mantle Flow
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地幔流板块生成的简单模型
DOI：
10.1111/j.1365-246x.1993.tb06993.x
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发表时间：
1993
影响因子：
2.8
通讯作者：
D. Bercovici
中科院分区：
文献类型：
--
作者：
D. Bercovici
本文用一个简单的非牛顿蠕动流模型来评价使低粘性地幔流变为板状的流变学类型。该模型描述了由源和汇驱动的浅层岩石圈运动。源代表扩张脊，而汇代表俯冲带;因此，源和汇也规定了地表磁场的极向分量。环形（走滑）分量的湍流场被发现通过thesolution的斯托克斯方程与非牛顿流变。作为该模式的第一个基本研究，Olson & Bercovici（1991）的二维矩形速度场的水平散度被用于源汇场。诱导流体流再现矩形板的程度被用来衡量不同流变学在产生板状流体流方面的成功程度。结果表明，幂律流变，即使在非常高的幂律指数ν的极限下，也只能产生适度的板状流变。例如，从正方形板导出的源-汇场的环向动能与极向动能之比最多为0.65，而完美正方形板的比率为1.0。此外，幂律流变学产生板状行为的能力似乎达到了渐进极限。这意味着即使在非常高的ν的极限下，板块构造也不可能由幂律流变学产生。一类流变学产生了明显更有希望的结果，这是由于采用幂律指数ν < 0的Carreau假塑性流变学。这类流变学中的一个是Whitehead & Gans（1974）的粘滑地震行为的连续介质模型，它本质上是ν = −1的Carreau方程。这类流变，称为粘滑流变，诱导一个正方形板的源-汇功能，可以高达0.9的环形极向动能比。这类流变学的粘度（或强度）分布也看起来更像板状，显示出相当均匀的高粘度区（伪板）和明显界定的低粘度区（伪边缘）。相反，即使是最非线性的幂律流变学产生空间变化的高粘度区域和相对平滑的低粘度裕度。粘滑流变学在板材生产中的较大成功归因于一种自润滑机制，在这种机制中，动量从高剪切区向低剪切区的转移被抑制。相反，即使在无限幂律指数的极限下，幂律流变学也能阻碍但不能阻止动量传递。这一特征对于将速度剖面锐化成板状剖面是必不可少的，这一点可以用一个简单的边界层理论来说明。关键词：板块构造，地幔对流，非牛顿流体，环极耦合。
SUMMARY A simple model of non-Newtoniancreepingflow is used to evaluate classes of rheologieswhichallow viscous mantle flow to becomeplate-like. The model describes shallow-layerlithosphericmotion driven by sources and sinks. The sources represent spreading ridges while the sinks rep-resent subduction zones; the sources and sinks thus also prescribe the poloidal component ofthe surface flow field. The toroidal (strike-slip) component of the flow field is found via thesolution of the Stokes equation with non-Newtonian rheology. As a first basic investigation ofthe model, the horizontal divergence from the two-dimensional rectangular velocity field ofOlson & Bercovici (1991) is used for the source-sink field. The degree to which the inducedfluid flow reproducesthe rectangularplate is used to measure the success of differentrheologiesin generating plate-like flows. Results indicate that power-law rheologies, even in the limit ofvery high power-law indexν, can only produce modest plate-like flow. For example, the ratioof toroidal to poloidal kinetic energy for a source-sink field derived from a square plate is atbest 0.65, whereas a perfect square plate has a ratio of 1.0. Moreover, the power-law rheologyappears to reach an asymptotic limit in its ability to produce plate-like behavior. This impliesthat plate tectonics is unlikely to arise from a power-law rheology even in the limit of very highν. A class of rheologies that yield significantly more promisi ng results arise from the Carreaupseudo-plastic rheology with the power-law index taken to be ν < 0. One rheology in thisclass is the continuum model for stick-slip, earthquake behavior of Whitehead & Gans (1974),which is essentially the Carreau equation with ν = −1. This class of rheologies, referred to asthe stick-slip rheologies, induces a toroidal to poloidal kinetic energy ratio for a square plates’ssource-sink function which can be as high as0.9. The viscosity (or strength) distribution forthis class of rheologies also appears more plate-like, showing fairly uniform high viscosity re-gions (pseudo-plates) and sharply defined low viscosity zones (pseudo-margins). In contrast,even the most nonlinear power-law rheology produces spatially varying high viscosity regionsand relatively smooth low viscosity margins. The greater success of the stick-slip rheologiesin producing plates is attributed to a self-lubricating mechanism in which the transfer of mo-mentum from regions of high shear to low shear is inhibited. In contrast, even in the limit ofinfinite power-law index, a power-law rheology can retard but never prohibit momentum trans-fer. This feature is essential to the sharpening of velocity profiles into plate-like profiles, whichis illustrated with a simple boundary-layertheory.Key words: Plate tectonics, mantle convection, non-Newtonian flow, toroidal-poloidal cou-pling.